Given:#" "color(brown)(4x+3y=-5)#......................(1)
#color(blue)("To find the x-intercept")#
The x-axis crosses the y-axis at #y=0# so all we need to do is substitute 0 for y and we are then able to determine x-intercept
Write equation (1) as #" "4x+3(0)=-5#
Divide both sides by 4 giving
#4/4 x=-5/4#
But #4/4 = 1#
#color(blue)(x_("intercept") =-5/4#
#color(blue)("To find the y-intercept")#
The y-axis crosses the x-axis at #x=0# so all we need to do is substitute 0 for x and we are then able to determine y-intercept
Write equation (1) as #" "4(0)+3y=-5#
Divide both sides by 3 giving
#" "3/3 y=-5/3#
But #3/3 = 1#
#" "color(blue)(y_("intercept")=-5/3)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Drawing the graph")#
Put a mark on the x axis at #x=-5/4#
Put a mark on the y axis at #y=-5/3#
Put a ruler on the graph and draw a line that passes through both these points. Extend the line to the edges of the graph.
#color(red)("////////////////////////////////////////////////////////////////////////////")#
#color(green)("If you so wish to, this is how you change the equation into the format of")#
#" "y=mx+c#
Subtract #color(blue)(4x)# from both sides
#" "color(brown)(4xcolor(blue)(-4x)+3y=-5color(blue)(-4x)#
#" " 0+3y=-4x-5#
Divide both sides by (same as #color(blue)(xx1/3)")"#
#" "color(brown)(3ycolor(blue)(xx1/3)=(-4x-5)color(blue)(xx1/3))#
#" "3/3xx y =-4/3x-5/3#
But #3/3 =1 # giving
#" "y=-4/3x-5/3#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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